Question

Знайти сторони прямокутника, якщо вони відносяться як 3:4 а діагональ дорівнює 10 см

Answer 1

Finding the Sides of a Rectangle with a Given Diagonal

To find the sides of a rectangle when the ratio between them is given and the diagonal is known, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the diagonal of the rectangle is the hypotenuse of a right triangle formed by the sides of the rectangle. Let's assume that the sides of the rectangle are represented by the variables '3x' and '4x', where 'x' is a constant. The diagonal of the rectangle is given as 10 cm.

Using the Pythagorean theorem, we can set up the following equation:

(3x)^2 + (4x)^2 = 10^2

Simplifying the equation:

9x^2 + 16x^2 = 100

25x^2 = 100

Dividing both sides of the equation by 25:

x^2 = 4

Taking the square root of both sides:

x = 2

Now that we have the value of 'x', we can find the lengths of the sides of the rectangle:

Length = 3x = 3 * 2 = 6 cm

Width = 4x = 4 * 2 = 8 cm

Therefore, the sides of the rectangle are 6 cm and 8 cm, respectively.